Planar lattice gases with nearest-neighbour exclusion

TL;DR

This paper applies the corner transfer matrix method to analyze planar lattice gases with nearest-neighbour exclusion, providing highly accurate numerical results for partition functions, densities, and correlations on various lattices.

Contribution

It introduces a numerical approach to precisely evaluate partition functions and correlations in lattice gases with exclusion constraints, including the hard-hexagon, hard-square, and honeycomb lattices.

Findings

Partition function per site computed to 43 decimal places for the square lattice.

High-accuracy estimates of density and near-neighbour correlations.

Numerical results for different lattice geometries and activity levels.

Abstract

We discuss the hard-hexagon and hard-square problems, as well as the corresponding problem on the honeycomb lattice. The case when the activity is unity is of interest to combinatorialists, being the problem of counting binary matrices with no two adjacent 1's. For this case we use the powerful corner transfer matrix method to numerically evaluate the partition function per site, density and some near-neighbour correlations to high accuracy. In particular for the square lattice we obtain the partition function per site to 43 decimal places.